We turn -5,12 into polar coordinates. It's a Pythagorean Triple so
r = 13 Ф=arctan(-12/5) + 180° ( in the second quadrant )
so -5 = 13 cos Ф, 12 = 13 sin Ф
12 sin x - 5 cos x = 6.5
13 sinФ sin x + 13 cos Ф cos x = 6.5
13 cos(x - Ф) = 6.5
cos(x - Ф) = 1/2
cos(x - Ф) = cos 60°
x - Ф = ± 60° + 360° k integer k
x = Ф ± 60° + 360° k
x = 180° + arctan(-12/5) ± 60° + 360° k
That's the exact answer;
x ≈ 180° - 67.38° ± 60° + 360° k
x ≈ 122.62° ± 60° + 360° k
x ≈ { 62.62°, 182.62°} + 360° k, integer k
It would be around 138 minutes which is 2 hrs and 18 min so it would be C).
Answer:
v=3i+8j
Step-by-step explanation:
The given the vector v has an initial point (-2,-6) and a terminal point of (1,2).
To find the components of vector v, we subtract the terminal points from the initial point to obtain.
v=<1,2>-<-2,-6>
v=<1--2,2--6>
v=<1+2,2+6>
v=<3,8>
As a linear combination of the standard unit vectors.
v=3i+8j
